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Bentuk sederhana dari (32p−2q2)−2(3p−2q5)−2​adalah ....

Pertanyaan

Bentuk sederhana dari open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent spaceadalah ....

Pembahasan Video:

Pembahasan:

Diketahui suatu eksponen open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space. Berdasarkan sifat bilangan berpangkat negatif yaitu a to the power of negative n end exponent equals 1 over a to the power of n maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell fraction numerator 1 over denominator open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses squared over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses squared end fraction end cell row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses squared over open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat pangkat dipangkatkan yaitu open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses squared over open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses squared end cell row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell fraction numerator open parentheses 3 squared close parentheses squared cross times open parentheses p to the power of negative 2 end exponent close parentheses squared open parentheses q squared close parentheses squared over denominator open parentheses 3 close parentheses squared open parentheses p to the power of negative 2 end exponent close parentheses squared open parentheses q to the power of 5 close parentheses squared end fraction end cell row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell fraction numerator 3 to the power of 4 cross times p to the power of negative 4 end exponent cross times q to the power of 4 over denominator 3 squared cross times p to the power of negative 4 end exponent cross times q to the power of 10 end fraction end cell end table

Berdasarkan sifat bilangan berpangkat pembagian yaitu a to the power of m over a to the power of n equals a to the power of m minus n end exponent sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell fraction numerator 3 to the power of 4 cross times p to the power of negative 4 end exponent cross times q to the power of 4 over denominator 3 squared cross times p to the power of negative 4 end exponent cross times q to the power of 10 end fraction end cell row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell 3 to the power of 4 minus 2 end exponent p to the power of negative 4 minus left parenthesis negative 4 right parenthesis end exponent q to the power of 4 minus 10 end exponent end cell row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell 3 squared p to the power of 0 q minus 6 end cell row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell fraction numerator 9 cross times 1 over denominator q to the power of 6 end fraction end cell row cell open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent space end cell equals cell 9 over q to the power of 6 end cell end table


Dengan demikian, Bentuk sederhana dari open parentheses 3 p to the power of negative 2 end exponent q to the power of 5 close parentheses to the power of negative 2 end exponent over open parentheses 3 squared p to the power of negative 2 end exponent q squared close parentheses to the power of negative 2 end exponent spaceadalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 9 over q to the power of 6. end cell end table

Jawaban terverifikasi

Dijawab oleh:

N. Puspita

Terakhir diupdate 07 Oktober 2021

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